I won’t answer for Charlie, but years ago I read about a shul in the Bronx that had services in a mosque. If I recall correctly, it was a struggling shul in a changed neighborhood (as are/were most neighborhoods in the Bronx), and they lost their building. I don’t remember the details (e.g. what part of the mosque’s building they used).
Since you call yourself Talmidchochom, perhaps you can tell us why it’s assur to daven in a mosque.